(A) 115.30-kyr-tuned time series (see Supplementary Table S4). (B) Multi-taper method spectral analysis (MTM) results, using three tapers and a time-bandwidth product of 2p. The calibrated periods of significant peaks are shown in kyr; these peaks achieve the 90% confidence level for both the MTM harmonic F-test and the AR1 red noise model (bold) or the AR1 noise model only (italics) (see Supplementary Fig. S11, Supplementary Table S5). (C) Evolutive power spectral analysis (EPSA) results, using a moving window of 1000 kyr, 3 tapers and a time-bandwidth product of 2p (see Supplementary Fig. S12). A linear trend was removed from each window prior to the EPSA. Letters E1-P mark the eccentricity, obliquity and precession cycles separately (see Supplementary Table S2). (D) Phases that are defined by the minima of the filtered 405-kyr components (in E). Horizontal dashed lines are phase boundaries. (E) Filtered δ13Ccarb time series for Majiashan section. Red and blue curves indicate short and long eccentricity cycles defined using bandpass filters of 0.0015–0.0028 cycles/m and 0.006–0.011 cycles/m, respectively. Black dotted lines show the instantaneous amplitude envelope of the δ13Ccarb short eccentricity signal. (F) Theoretical eccentricity from La10d from 249.0 Ma-247.0 Ma. Red and blue curves indicate short and long eccentricity cycles. Note that La10d eccentricity curves are reversed to illustrate relationship between δ13Ccarb maxima and eccentricity minima in Phase 6 marked by blue shading (see Supplementary Table S4). Radioisotopic dates from ref. 32,33. Correlation of latest Spathian interval constrained by radioisotopic ages shown by grey shading. The large silhouettes to the right of Panel F are marine reptiles; the small silhouettes to the right of Panel F (and one medium silhouette) are fish.